Logic of the set analyzer

Hi;
I'll start from an example.
There's a given set of positive integers: {2, 4, 6, 8, 10}. The problem is to estimate a (relative) probability for any number (not included into the set) to follow the logic of the set. For the example above, the probable logic is: even numbers only. Following this conclusion one can say that numbers 12, 14, 16, 18, 20 have the same and higher probability (=1) to follow set's logic, then numbers 1, 3, 5, 7, 9 (probability=0).
But the problem can be not so simple for a different set of data. E.g.: the set is {1, 3, 7, 11, 19, 21, 28, 31, 47, 53, 62, 69, 75, 76, 82, 98}. The problem is to estimate the relative probability for numbers 700, 800 and 900 to follow the logic of the set.

You could throw in the numbers you have into a statistical estimation routine and run a probability estimation program like LOGIT or PROBIT. Examples of this kind of software are Limdep, SAS, Stata, EViews, Mathematica, Maple, etc. The model I would use would be:

Binary 0 or 1 = Probit(char1, char2, ..., charN)

where each "char" is a distinct characteristic of the numbers in the set. In your even numbers example, N=1 and char1 = 1 if the number is even, char1 = 0 if it is odd.

For the set {1, 9, 25, 49, 81}, N=2 and char1 = 1 if the number is a perfect square, char = 0 if it is not a perfect square, char2 = 1 if the number is odd, char2 = 0 if it is even.

Thanks a lot, EnumaElish.
The keywords were LOGIT and PROBIT. And I found a lot of software in the Inet (e.g.: http://www.oswego.edu/~economic/econsoftware.htm). I'll try to test the soft on my data. Hopefully, some of it will return a good result.
Thanks again,
Max.